however, do any of you think this can also be damaging to recovery efforts as well?
Only if you were LRTing during the marriage and totally ignoring your spouse, for which reason they had a problem with you, in which case, it appears to them that you haven't changed.
Could it possibly be perceived to the spouse that he/she is no longer important?
Let's hope so. That's one of the ideas behind it, that we're more involved with our own lives and can be happy without the spouse. But look at it another way: showing the WAS how dedicated we are to them and the relationship by engaging typically in clingy pursuing behaviors and declarations of our commitment to our vows, doesn't work but it does push them further away. Understanding the reasons why that is so, helps us in understanding why LRT can be effective.